制約

入力

出力

入力例 1

出力例 1

Yes

例えば、(0,0), (0,1), (1,1), (1,2), (1,1), (1,0), (1,1) と移動すればよいです。

入力例 2

1
2 100 100

出力例 2

No

(0,0) にいる状態から 2 秒後に (100,100) にいるのは不可能です。

入力例 3

2
5 1 1
100 1 1

出力例 3

No

Score : 300 points

Problem Statement

AtCoDeer the deer is going on a trip in a two-dimensional plane.
In his plan, he will depart from point (0, 0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i,y_i) at time t_i.

If AtCoDeer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1,y), (x-1,y), (x,y+1) and (x,y-1).
Note that he cannot stay at his place.
Determine whether he can carry out his plan.

Constraints

1≤N≤10^5

0≤x_i≤10^5

0≤y_i≤10^5

1≤t_i≤10^5

t_i<t_{i+1} (1≤i≤N-1)

All input values are integers.

Input

Input is given from Standard Input in the following format:

Nt_1x_1y_1t_2x_2y_2:t_Nx_Ny_N

Output

If AtCoDeer can carry out his plan, print Yes; if he cannot, print No.

Sample Input 1

2
3 1 2
6 1 1

Sample Output 1

Yes

For example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).